Researchers from the University of Patras, Greece, and the Okinawa Institute of Science and Technology (OIST), Japan, complement a 100-year-old theory describing the stress-induced transition of elastoviscoplastic (EVP) materials from solid to liquid behavior, such as mud, crude oil, paste, and blood. According to the research team, led by Amy Shen at OIST and John Tsamopoulos at Patras, while current theory assumes that the solid state is undeformable, their experimental work combined with simulations show that the elasticity property in the materials’ solid state is key to the transition. They report their study in a recent issue of the Proceedings of the National Academy of Sciences (PNAS). 

An elastoviscoplastic fluid or material behaves like an elastic solid when exposed to a stress that is below a critical value, namely the yield stress (τy); above it, it flows like a complex fluid. Such materials are also known as yield-stress fluids. “[Having] a fundamental understanding of how EVP materials flow is very useful, especially in biomedical science and geophysics,” says Shen in a news release. For example, she says, blood behaves like a solid at rest, but flows like a liquid in arteries. Some 3D-printed tissues and scaffolds can have EVP properties.

Previous experimental research on EVP materials measured their behavior under shear flow, obtained when layers of fluid slide past each other. However, in industrial processing, the fluid is stretched—called “extensional flow.”  In fact, very little of the normal stresses developed in these materials is known. “Accurate modeling of elastoviscoplastic materials enables us to simulate, control, design, and optimize processes that include a wide variety of such materials with quite different properties: from gel-like materials that can sustain large deformation prior to yielding—like mayonnaise, hair gels, body care creams, and waxy crude oil—to brittle materials like fresh cement, snow avalanches, lava, or even the surface of a planet when a comet crushes upon it,” Tsamopoulos tells MRS Bulletin.

In order to get insights into the elongational and yielding properties of EVP materials, the research team turned to a new microfluidic device, an optimized shape cross-slot extensional rheometer (OSCER). They examined a commonly known biomedical polymer called Pluronic. In addition, the research team simulated the flow of the Pluronic solution as well as another EVP material called Carbopol, a gel often used in hand sanitizers. The team showed that complex patterns arose in the flow, which included the presence of solidified regions surrounded by the liquid-state. Their findings are in good agreement with the experiments.

“When we put pressure on the two inbound channels, which were located opposite to each other, the solution was pushed toward the center point and it came out of the other two channels. The resulting flow has a point at the center where the velocity goes to zero. In the two outbound channels, we generated an extensional flow where the fluid was stretched,” says Simon Haward of OIST in a news release.

In the experiment, with a flow rate of 0.22 s^-1 and plastic number 0.88 (where a plastic number of 0 is a fluid-like response), which is close to 1—an elastic solid-like response even though the material is in a liquid state around the stagnation point—illustrates pure elongation of the material at that area. The researchers also found good agreement between their simulation and experimental results when they increased the extension rate until they reached a flow rate of 90 s^-1 and plastic number of 0.52.

The green and yellow particles move from the liquid region to the unyielded region (blue) where they undergo a solid body rotation during elastoviscoplastic flow. Credit: OIST

Tsamopoulos explains to MRS Bulletin that according to the ideal (previous) viscoplastic theory, the ratio of the value of the tensile stress plateau measured in planar extension to the shear stress plateau measured in simple shear equals to 2, irrespective of the properties of the material. “We show that materials which exhibit pronounced elasticity can deform significantly prior to yielding and in such cases the so-called ‘yield stress Trouton ratio’ will attain values larger than 2,” says Tsamopoulos; “Practically, this means that elastoviscoplastic materials with pronounced elasticity can store energy and thus, unexpected phenomena can be observed when this energy is released during their deformation and flow, which would not be observed in respective flows of viscoplastic or Newtonian fluids.”

According to Tsamopoulos, some of the most notable examples of unexpected phenomena uncovered within the past few years are the characteristic cusped shapes of bubbles rising in gels and the loss of fore-aft symmetry in the flow field around a sedimenting particle in a gel. “These and other observations hinted that something important was missing from the standard viscoplastic theory,” he says. This led the group to believe that elasticity is a key property of such materials and should necessarily be included when modeling and predicting the behavior of such materials in various processes.

Tsamopoulos tells MRS Bulletin, “To classify these materials, we defined a simple dimensionless number (yield strain) that gives a measure of how the material is going to behave: materials with low yield-strain values are expected to behave more like ideal viscoplastic materials, while materials with high yield-strain values are expected to exhibit a complex rheological behavior, leading to unexpected phenomena.”

In essence, the study showed that experiments and simulations conducted under pure extension provide fundamental information on the behavior of these EVP materials. The yield strain of the material was found to govern the transition dynamics from the solid state to the liquid state. The current standard theory needs to be modified to account for deformation in the solid-like state prior to yielding and flow.

Read the article in Proceedings of the National Academy of Sciences.